Related papers: Photonic implementation of Majorana-based Berry ph…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
A fundamental symmetry of the non-Hermitian operators describing wave-propagation in time-varying media imbue such systems with non-trivial topology. This topology may be measured directly in a wide range of experimental settings as a…
Despite their apparent simplicity, coupled oscillators exhibit surprisingly complex phenomena. Two notable examples are Berry phase (a geometric or topological aspect of the oscillators' memory) and non-Hermiticity (the often…
Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models.…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
Non-Abelian anyons--particles whose exchange noncommutatively transforms a system's quantum state--are widely sought for the exotic fundamental physics they harbor as well as for quantum computing applications. There now exist numerous…
The well-known geometric phase present in the quantum adiabatic evolution discovered by Berry many years ago has its analogue, the Hannay phase, in the classical domain.We calculate the Berry phase with examples for quantum hermitian and…
We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric…
Quantum phase transitions are intriguing and fundamental cooperative phenomena in physics. Analyzing a superconducting nanowire with spin-dependent non-Hermitian hopping, we discover a topological quantum phase transition driven by…
Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, we construct a Z_N rotor model that realizes a self-dual Z_N Abelian gauge theory. We find…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana…
If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in…
Berry phases have long been known to significantly alter the properties of periodic systems, resulting in anomalous terms in the semiclassical equations of motion describing wave-packet dynamics. In non-Hermitian systems, generalizations of…
Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable…
We study phase diagrams of charge-conserving `class A' non-interacting fermions, focusing on the trivial phase in various dimensions. Such phases are usually termed `featureless' to distinguish them from those others with either…